Geometric formulas of linear perspective

10 years ago i tried (as an artist) to solve the problem of how to translate the 3 dimensional cartesian coordinate onto the 2 dimensional surface with the precise foreshortening. i've only ever figured out 3 formulas for 3 different standpoints... then i gave up. now i recollected my notes, and put them on line.

the linear perspective developed since the renaissance has never been complete. these 3 formulas are the only completed one i know of. can any math persons figure out the algebraic situation behind this geometric formulation of the translation of 3 d onto the 2 d?